Bordwells Anomaly

The equilibrium constant for a proton transfer reaction from a series of proton donors (SH) to base (B) (Equation 18) has a peq value of unity for the Bronsted dependence on the pX of SH (pX, ). 

Reference to Chapter 2 (Section 2.4) indicates that Pf and p are governed by Equation (20) which is general and applies to coefficients of other free energy relationships. 

Thus in the Hammett format Peq = Pf - Pr and in the normalised (Leffler) format Ugq = a, - a,. The parameter Ugq is unity and Uf and should both therefore be numerically less than 1 because of the negative sign of a,.. 

Bordwell and his co-workers discovered that the formation of the pseudo-base from nitromethane in hydroxide ion solutions (Equation 21) has a Pf of 1.28 and a p q of 0.83 giving rise to an a/ of 1.54. Similarly the ttf values for reaction of bases with other nitroalkanes are greater than unity also violating the Leffler assumption. 

Because it is the slope of a plot of logXjq versus log/f The value of Uf is given by Pf/pe,. 

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The equation breaks down when AGq < -4AGo when a becomes negative and when AG > 4AGo when a exceeds 1. This is not an explanation of Bordwell s anomaly because the breakdown criteria correspond to two chemically impossible structures where the cross-over points occur at bond lengths less than those in the relaxed states. The cross-over is illustrated for the case AG < -4AG in Figure 14. 

Current thought is that the anomalous parameters reflect an unusual transition state where there is no monotonic change from ground to product states. Bordwell considers that the anomalies arise from the rehybridisation required as well as the proton transfer in passing from nitroalkane to aci-species (Eqn. 37) [29c]. 

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